WATER RESOURCES RESEARCH, VOL. 47, W02515, doi:10.1029/2010WR009547, 2011
Using time domain and geographic source tracers to conceptualize
streamflow generation processes in lumped rainfall-runoff models
Christian Birkel,1,2 Doerthe Tetzlaff,2 Sarah M. Dunn,1 and Chris Soulsby2
Received 13 May 2010; revised 11 November 2010; accepted 2 December 2010; published 11 February 2011.
[1] The temporal dynamics and geographical sources of streamflow were conceptualized in
a lumped rainfall-runoff model (isoSAMdyn) using isotopic and geochemical tracers derived
from a field study in a 3.6 km2 upland catchment in Scotland. High-resolution (daily)
sampling of stable isotopes in precipitation and streamflow over a hydrological year,
supplemented by fortnightly sampling of groundwater and riparian saturation zones,
allowed hypotheses of runoff generation processes to be tested. These were conceptualized
in a previously developed model (SAMdyn) based only on geochemically defined
geographic source tracers, which showed that the nonlinear dynamic expansion and
contraction of riparian saturation areas is the dominant mechanism for storm runoff
generation in the catchment. While SAMdyn resulted in reasonable simulation of
streamflows and alkalinity (as a source tracer), it was unable to reproduce the rainfall-runoff
dynamics of deuterium (2 H). Using the model in a learning framework, incorporation of
parameters for passive storage in catchment hillslopes and groundwater mixing in riparian
saturation zones, along with associated isotopic fractionation, improved 2 H simulations in
stream water and the major catchment water stores. The resulting model provided a
conceptualization of rainfall-runoff processes that broadly reconciled hydrometric data and
geochemical and isotopic signals. However, in this particular catchment, fractionation of
water in surface saturation zones appears to be a complex process that prevents the
simulation of short-term isotope dynamics in the stream during the summer period.
Citation: Birkel, C., D. Tetzlaff, S. M. Dunn, and C. Soulsby (2011), Using time domain and geographic source tracers to conceptualize
streamflow generation processes in lumped rainfall-runoff models, Water Resour. Res., 47, W02515, doi:10.1029/2010WR009547.
1.
Introduction
[2] Conceptualization of streamflow generation processes and integration into rainfall-runoff models remains a
major research challenge in catchment hydrology [Lischeid, 2008; Tetzlaff et al., 2008a]. Despite more than a decade of closer collaboration between field experimentalists
and modelers [e.g., Seibert and McDonnell, 2002], there
remains much debate over what is the appropriate level of
model parameterization and how best to ensure that models
give the right answers for the right reasons [Kirchner,
2006]. Recently, the integration of field-derived tracer data
in rainfall-runoff models has been shown to be a potentially
useful research tool in this regard [e.g., Uhlenbrook and
Leibundgut, 2002; Dunn et al., 2003]. Geochemical tracers
provide insights into the geographical sources of streamflow [e.g., Hooper, 2001] and isotopic (or other conservative) tracers into the temporal dynamics of runoff processes
[e.g., Pearce et al., 1986]. However, it is not uncommon
that hydrometric, geochemical, and isotopic signals provide
apparently contradictory insights into catchment function
1
Macaulay Land Use Research Institute, Aberdeen, UK.
Northern Rivers Institute, School of Geosciences, University of Aberdeen, Aberdeen, UK.
2
Copyright 2011 by the American Geophysical Union.
0043-1397/11/2010WR009547
[Kirchner, 2003] which can be difficult to reconcile in
terms of understanding and modeling the hydrological
response [McDonnell et al., 2007].
[3] Until relatively recently, logistical and financial constraints often resulted in marked differences in the temporal
resolution of hydrometric data (typically 15 min) and isotopic tracer data (often weekly) [Kirchner et al., 2004].
Improvements in the reliability of automatic water samplers and, more importantly, the recent availability of laser
spectroscopy facilitate high-resolution daily or subdaily
sampling over long periods at relatively low cost [e.g.,
Lyon et al., 2009; Birkel et al., 2010b]. This provides a rich
resource for incorporating field-based insights in hydrological models, which may have previously been masked by
coarse sampling time steps [Berman et al., 2009].
[4] While both geochemical tracers and stable isotopes
have been used to constrain and evaluate rainfall-runoff
models [e.g., De Grosbois et al., 1988; McGuire et al.,
2006; Fenicia et al., 2008], they have rarely been used
simultaneously. Yet such dual-tracer approaches have
powerful potential in hypothesizing both the sources of runoff and their temporal dynamics [e.g., Katsuyama et al.,
2009] and testing these hypotheses within a modeling-based
learning framework [Vaché and McDonnell, 2006; Beven,
2007; Dunn et al., 2008]. This approach also has the possibility of exploring the nature of storage-discharge relationships, which are usually parameterized within rainfall-runoff
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models but may provide fundamental insights into catchment
function [e.g., Kirchner, 2009]. For example, isotope studies
have shown that the total catchment storage is likely to be
much greater than the dynamic storage inferred by hydrometric data alone [e.g., Soulsby et al., 2009], which needs to
be invoked to explain nonlinearity in rainfall-runoff
responses in relation to antecedent conditions [e.g., Dunn
et al., 2010]. This larger, more passive (often called immobile) water storage has long been cited as an explanation for
the observed damping of streamflow isotope signatures compared to precipitation [Barnes and Bonell, 1996] and the
long tailing of residence time distributions [Kirchner et al.,
2000] by retaining water for long periods before release
[Spence, 2007]. A better understanding of the spatial distribution of water stores and temporal dynamics of water
release mechanisms in catchments is therefore needed to
enhance the conceptualization of catchment functioning in
rainfall-runoff models [Soulsby et al., 2008]. Again, dualtracer applications in conceptual hydrological models have
utility if tracer data from different hydrological stores can
help to internally verify a model and the applied storage conceptualization [Seibert and McDonnell, 2002; Tetzlaff et al.,
2008b].
[5] In different geographical regions, the relationships
between landscape organization and catchment hydrological response vary as the dominant runoff generation processes change [e.g., Tetzlaff et al., 2009a]. Differences in
topography, soil cover, and climate interact to govern the
catchment hydrological response [Hrachowitz et al., 2009].
In glaciated landscapes such as the Scottish Highlands, the
catchment soil cover reflects the interactions between climate, topography, parent material, and land use. Soil
hydrological characteristics play a key role in controlling
catchment rainfall-runoff responses [Soulsby et al., 2006].
Previous field and modeling studies in such environments
have shown the importance of dynamically expanding and
contracting riparian saturation zones, often related to
organic-rich peaty (histic) soils which have developed on
poorly drained drift deposits [Seibert et al., 2003; Birkel
et al., 2010a]. Riparian saturation zone dynamics reflect
catchment connectivity and control the generation of quick,
near-surface runoff processes [Tetzlaff et al., 2007a]. As
such, runoff mechanisms are dependent on the linkages
between the saturated areas and their surrounding hillslopes, and the hydrological response is highly nonlinear in
relation to antecedent conditions [Tetzlaff et al., 2008a].
Therefore, understanding the role of the riparian zone on
nonlinear runoff generation and mixing of waters originating from different sources is crucial to modeling water and
solute transport [Seibert et al., 2009].
[6] Here we extend earlier work in the Girnock, a Scottish upland catchment, which used field-based process
insights to develop a tracer-aided rainfall-runoff model
(SAMdyn) to simulate flow and geographical source area
tracer responses on the basis of nonlinear saturated area dynamics [Birkel et al., 2010a]. The present study sought to
incorporate high-resolution time domain tracers (stable isotopes) as a further means of model evaluation in terms of
the temporal dynamics of rainfall-runoff processes. The
study combined field and modeling components with the
following objectives : First, to characterize the isotopic and
geochemical signature of the major water stores and fluxes
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of the catchment hydrological system over a hydrological
year. Here particular attention was focused on the acquisition of high-resolution (daily) isotope analysis of precipitation and streamflow to understand the temporal dynamics
of rainfall-runoff processes. Second, using these data to
underpin the evolution of the original SAMdyn model to be
able to simulate the temporal dynamics of both time domain and geographic source tracers in major catchment
stores and fluxes within an internally consistent conceptual
rainfall-runoff model (isoSAMdyn). Finally, we seek to outline the challenges and limitations of such a dual-tracer
approach in conceptual modeling.
2.
Study Site
[7] The Bruntland Burn (BB) is a subcatchment of the
Girnock Burn experimental catchment, which drains into
the River Dee and is located in the Cairngorms National
Park, Scotland (Figure 1). Full details of the Girnock catchment are given by Tetzlaff et al. [2007a] and Soulsby et al.
[2007]. The BB subcatchment drains 3.6 km2 with a mean
altitude of 350 m above sea level (asl). Annual precipitation,
mainly from westerly frontal systems, is around 1000 mm,
with the summer months (May – July) generally being driest
[Tetzlaff et al., 2005]. Annual runoff is about 600 mm. The
landscape has been glaciated and has typical landforms
such as steep slopes and wide valley bottoms. Land cover is
dominated by heather (Calluna vulgaris) moorland (20%),
peat bogs (13%), and an area of commercial forestry (34%)
on the steeper hillslopes near the catchment outlet. The eastern hillslopes are underlain by granite, which occupies 46%
of the catchment. The bedrock on the western and southern
flanks (45% of the catchment) is dominated by schists and
other metamorphic rocks (9%) [Soulsby et al., 2007]. Fractured bedrock outcrops occupy 29% of the catchment area,
particularly at high elevation, and are likely to be important
recharge zones [Tetzlaff et al., 2007b].
[8] Much of the catchment’s lower slopes are covered by
glacial drift deposits, particularly low-permeability till in
the valley bottoms, upon which hydrologically responsive
gley and peat soils (covering about 61% of the area) have
formed. These roughly map on to the area of maximum saturation (Figure 1) and are well connected to the stream
channel network [Tetzlaff et al., 2009b]. Process studies
have shown that such soils are near saturation for much of
the year and the saturated areas dynamically expand and
contract according to wetness conditions ranging between
2% and 40% of the total area [Birkel et al., 2010a]. These
saturation areas generate substantial amounts of saturation
excess overland flow and shallow lateral flow in organic
surface horizons. The second most common soil unit (39%
of the catchment) comprises freely draining brown earths
(cambic) on steeper hillslopes which generally remain unsaturated. Vertical water movement mainly facilitates
groundwater recharge in such soils [Soulsby et al., 1998].
Soulsby et al. [2005] have indicated that a portion of
groundwater recharge probably moves quickly through
shallow fracture systems [e.g., Shand et al., 2006] or freely
draining drift deposits to discharge into valley bottom
areas. This discharge emerges either as hillslope seepage
return flow into the area of saturated peaty soils or through
the bed and banks of the stream [Malcolm et al., 2006].
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Figure 1. Bruntland Burn catchment topography, sampling locations, and mapped maximum and minimum saturation area extent (Stream gauge grid reference: NO 324956).
3.
Data Sources
3.1. Hydrology
[9] Discharge (15 min resolution) was measured in a natural rated section (Figure 1) using an Odyssey capacitance
rod. Rainfall (15 min resolution) was recorded by a tipping
bucket gauge (HOBO) sited at an altitude of 300 m asl near
the catchment outlet (Figure 1). Actual evapotranspiration
(ET) was estimated by a Penman-Monteith equation
adjusted to aerodynamic and canopy roughness characteristics of the study site [Dunn and Mackay, 1995]. Meteorological data were used from stations located 20 km from
the catchment (operated by the Macaulay Land Use
Research Institute) and located 3 km from the catchment
(operated by Marine Scotland).
3.2. Stable Isotopes
[10] Daily precipitation and stream isotope sampling was
undertaken using ISCO 3700 automatic water samplers
from 1 September 2008 through 6 October 2009 (Figure 1).
Stream samples were taken instantaneously at 8:00 A.M.,
and precipitation samples were taken at the same time but
represented accumulations over the preceding 24 h (Table
1). During the winter (December – February), only weekly
stream samples were possible because of a malfunction of
the automatic sampler during frosts. Paraffin oil was
applied to the sample bottles to avoid evaporation losses
[International Atomic Energy Agency, 2009]. The deuterium (2H/1H) and oxygen-18 (18O/16O) ratios were simultaneously determined with a Los Gatos Research DLT100
laser diode water isotope analyzer using a standard analytical protocol [Lis et al., 2008; Birkel et al., 2010b]. Data
were transformed into the notion (2 H and 18 O in %)
according to Vienna standard mean ocean water (VSMOW)
standards. We analyzed both 2 H and 18 O, but because of
the interdependence of both isotopes, greater precision, and
variability over wider range, we only consider 2 H for the
model simulations. Average precision for the instrument
was 0.63% and 0.25% for 2 H and 18 O, respectively.
[11] In addition, fortnightly groundwater samples were
taken at two deep wells and from a spring at a lower hillslope seepage (Figure 1). Overland flow waters were
sampled at three different locations of perennial saturation,
again on a fortnightly basis, but starting slightly later on 1
January 2009 (Table 1). Snow samples were taken and analyzed for stable isotopes during a 2 week period of snow in
the catchment at the end of February 2009.
3.3. Geochemistry
[12] We also analyzed stream, groundwater, and saturated area samples for alkalinity on a weekly or fortnightly
basis. Unfortunately, daily stream samples could not be
used because of potential contamination by the paraffin. Alkalinity (in eq L1) is a measure of the acid-neutralizing
capacity of waters and was determined by acidimetric titration (0.005 M H2SO4) to the end point pHs 4.5, 4, and 3
using an Eppendorf pipette with a precision of 61% [Neal
et al., 1997]. It essentially reflects the geographic sources
of water: In many Scottish upland catchments, low flows
are dominated by high alkalinities, showing a clear geological imprint of groundwater, while storm runoff is derived
from acidic, upper soil horizons with alkalinities close to
zero [Soulsby et al., 2007]. The close relationship between
measured stream alkalinity concentrations and discharge
(2003 – 2008, R2 > 0.8) has been demonstrated for the Girnock by Tetzlaff et al. [2008b]. This has been used as a basis for parameterizing alkalinity in groundwater and soil
water sources in the SAMdyn model, as described by Birkel
et al. [2010a].
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Table 1. Sampling Resolution and Collection Method
Hydrology
Geochemistry
Isotopes
4.
Component
Resolution
Method
Precipitation
Discharge
Actual ET
Stream alkalinity
Saturation zone alkalinity
Groundwater alkalinity
Precipitation 2 H
Snow 2 H
Stream 2 H
Groundwater 2 H
Hillslope spring 2 H
Saturation zone 2 H
15 min
15 min
Hourly
Weekly
Sporadic
Sporadic
Daily
Sporadic
Daily (8:00 A.M.)
Fortnightly
Fortnightly
Fortnightly
Tipping bucket
Rating curve
Penman-Monteith
Spot
One location
One location
Accumulated
Spot
Spot
Two locations
One location
Three locations
Model Development
4.1. Model Concept
[13] A daily rainfall-runoff model, the dynamic saturation area model (SAMdyn), has been developed for the Girnock catchment and is fully described by Birkel et al.
[2010a]. Briefly, the model is a lumped, conceptual, traceraided water balance model that simulates daily runoff. The
model is driven by daily precipitation inputs (Pup, Psat)
equivalent to the difference of precipitation rate and actual
evapotranspiration rate into a conceptualization that
dynamically links hillslope, saturation area, and groundwater reservoirs (Figure 2a). The dynamic structure of the
model uses an empirically based time series of an estimated
saturation zone extent (dyn_fSAT) calibrated against the
GPS-mapped saturated catchment area to dynamically vary
the storage volumes according to the wetness condition,
where a greater wetness results in a smaller hillslope storage area (Aup) and expanded saturation areas (Asat). A 7 day
antecedent precipitation exponential decay function was
found to best represent the wetness conditions and resulting
saturation zone extent in the Girnock catchment.
[14] A water balance is calculated at each time step for
the hillslope Sup, groundwater Sl, and saturation area storage Ssat of the SAMdyn model:
SupðtÞ ¼ Supðt1Þ þ ðPupðtÞ ETupðt1Þ ÞAup
i
Rðt1Þ Qupðt1Þ t;
ð1Þ
SlðtÞ ¼ Slðt1Þ þ ðRðtÞ Qlðt1Þ Þt;
ð2Þ
h
SsatðtÞ ¼Ssatðt1Þ þ QupðtÞ Qsatðt1Þ þ ðPsatðtÞ
ETsatðt1Þ ÞAsat t;
ð3Þ
where R (m3s1) is recharge to the lower storage Sl (m3);
Pup and Psat (m s1) are precipitation input into the total
hillslope storage Sup (m3) and saturation area storage Ssat,
respectively; ET is actual evapotranspiration (m s1); and
the dynamic Aup and Asat are in m2. Total discharge Q
(m3s1) is the sum of the discharge from both the saturation
area storage Qsat and lower groundwater storage Ql. Discharge from the hillslope Qup (m3s1) is routed into the saturation area storage Ssat (Figure 2a).
[15] The following equations define the linear storagedischarge fluxes from the upper (Sup) and lower storage (Sl):
Figure 2. (a) Model concept of the original dynamic saturation area model (SAMdyn) enabled to simulate isotope mixing and (b) the reconceptualized SAMdyn model with additional passive storage, groundwater return flow, and fractionation processes (isoSAMdyn).
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Qup ¼ Sup k1 ;
ð4Þ
R ¼ Sup r ;
ð5Þ
Q1 ¼ S1 k2 ;
ð6Þ
where k1, k2, r, and c (s1) are linear scaling parameters.
The nonlinear saturation area storage (Ssat) is defined as
1þ
Qsat ¼ Ssat
c;
ð7Þ
where is a dimensionless nonlinearity parameter.
[16] To simulate the alkalinity concentration of the main
water fluxes in the model, discharge-based functions were
implemented into the saturation area and groundwater
zones so that dynamic concentrations of Qsat and Ql could
be derived. These were based on empirical measurements
in the catchment as described by Birkel et al. [2010a]. The
estimate alkalinity concentrations (eq L1) for the saturation zone (Alkns) and groundwater runoff sources (Alkgw)
in the SAMdyn model are
Alkns ¼ 140Q0:55
; R2 ¼ 0:82;
sat
ð8Þ
Alkgw ¼ 750e1:2Ql ; R2 ¼ 0:93 :
ð9Þ
[17] For the present study, the SAMdyn model was
enhanced to incorporate isotope tracers directly linked to the
water fluxes of the reservoir conceptualization. The isotope
simulations are driven by daily precipitation and associated
deuterium 2 H signature equivalent to the difference of precipitation rate and evapotranspiration losses. This filters
minor precipitation events from effectively reaching the hillslope and saturation zone storage. The model assumes instantaneous and complete mixing in the storage routine. This
is represented by the total isotope tracer balance equation:
dðcSÞ
¼ AðcP P cETÞ cQ ;
dt
ð10Þ
where S is total storage (m3), ET is total evapotranspiration
(m s1), cP is the isotopic tracer composition (%) in total
rainfall P (m s1) over the total catchment area (m2), and c
is the isotopic tracer composition (%) in the reservoir.
Equation (10) allowed simulation of discharge and, most
importantly, 2 H as a time domain tracer, as well as alkalinity as a geographic source tracer.
[18] The simulated tracer stream signature 2 HQ (%) is
calculated via a weighted mean of saturation area and lower
groundwater storage tracer (2 HQsat, 2 HQl) and water
(Qsat, Ql) flux:
2 HQ ¼ ½ð2 HQsat Qsat Þ þ ð2 HQ1 Q1 Þ =Q :
ð11Þ
[19] It should be noted that the simulated 2 H values
2 HQup, 2 HQsat, and 2 HQl can be compared to the measured signatures collected from the hillslope spring, the saturation zone, and the groundwater in wells, respectively.
These comparisons provide a means for evaluating the internal isotope dynamics of the model as well as the outputs
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in streamflow. The time series were looped over 5 years for
the model to warm up because of the relatively short study
period. This facilitated the definition of the initial storage
values and validation of the internal water balances.
4.2. Model Calibration and Evaluation
[20] For evaluation of the rainfall-runoff simulations, the
Nash-Sutcliffe (NS) efficiency [Nash and Sutcliffe, 1970]
and volumetric error (VE) criteria [Criss and Winston,
2008] were used as performance measures. For simulation
of isotopes and alkalinity the coefficient of determination
R2 and the NS criterion were applied. The behavior of the
model was evaluated using a stepwise, multicriteria calibration [Khu et al., 2008] using tracer data in addition to
discharge.
[21] 1. Monte Carlo (MC) random sampling with 100,000
iterations was used to assign parameter values to model simulations. Efficiency criteria for discharge and both tracers
were evaluated for each iteration of the MC run.
[22] 2. On the basis of these results, efficiency criteria
thresholds for discharge and tracers were subjectively
established to maximum values for which it was still possible to identify acceptable parameter sets for all selected criteria. Model parameters were accepted as behavioral only
when the following criteria were adhered to: (1) discharge
Q with thresholds of QNS > 0.6 and QVE > 0.75, (2) stream
alkalinity Alk with AlkNS > 0.6, (3) stream deuterium
2HQ with NS > 0.2 and R2 > 0.4, and (4) saturation area
deuterium 2 HQsat with R2 > 0.4 (compared with the measured 2H in saturation area).
[23] 3. We attempt to reduce the subjectivity in the definition of behavioral parameter thresholds [Stedinger et al.,
2008] by taking additional 2 H data which reflects information on the internal state of the system into the calibration
procedure [Winsemius et al., 2009]. The goal is to internally constrain the model to be consistent with measured
data [e.g., Seibert and McDonnell, 2002; Kirchner, 2006].
Therefore, model runs were accepted as behavioral only
when the following criteria were additionally adhered to:
(1) an internal water balance error below 50 mm yr1, (2)
simulated hillslope 2 HQup of mean measured 2 H in the
shallow spring plus or minus analytical error (0.63%), and
(3) simulated groundwater 2 HQl of mean measured 2 H in
the deeper groundwater wells plus or minus analytical error
(0.63%).
[24] 4. The 5th and 95th percentiles of simulated discharge, alkalinity, streamflow 2 H, hillslope spring 2 H,
groundwater well 2 H, and saturation area 2 H at each time
step, across all acceptable parameter sets, were used to
define simulation envelopes representing uncertainty for
flow and tracer simulation.
4.3. Parameter Identifiability
[25] Parameter identifiability was assessed to evaluate
model hypotheses of catchment functioning and processes
and whether parameter values were constrained by the data
introduced additionally to discharge. The commonly used
regional sensitivity analysis (RSA) was applied to evaluate
how changes to model parameters might affect model predictions [Hornberger and Spear, 1981]. The uniformly
sampled parameter space for initially unconstrained parameter ranges was compared against the parameter space
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generated during model calibration using additional data to
discharge. This procedure reflects the effect of constraints
imposed on model parameters through data. The initial parameter space was sampled over a range from 0 to 1 for the
five flow model parameters (k1, k2, r, c, and ) and from 0
to 5000 for the isotope mixing parameter upSd. The partitioning of the parameter space in behavioral and nonbehavioral simulations as suggested for RSA was performed
according to the proposed multicriteria calibration (see section 4.2). The difference between the threshold criteria and
each accepted performance measure was used to calculate a
cumulative efficiency (cum Eff). The cumulative efficiency
over the parameter ranges indicates parameter identifiability:
A straight line indicates poor identifiability within the range
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and deviations indicate regions of identifiability. Higher gradients indicate clustering of behavioral simulations.
5.
Tracer Hydrology of the Bruntland Burn
[26] Over the 13 month study period we observed
slightly (5%) drier conditions than the long-term average.
The autumn and early winter of 2008 was a wet period,
though late December was dry, and precipitation was greatest between January and February 2009 (Figure 3a). The
greatest flow occurred in February in response to a rainfall
event falling on a melting snow pack (Figure 3c). Drier
conditions followed in spring (March – April), but the
summer of 2009 was wet, preceding a dry September.
Figure 3. (a) Mean daily precipitation (P), (b) mean daily actual evapotranspiration (ET), (c) mean
daily discharge (Q), (d) 2 H deuterium signatures in daily precipitation and stream response (%), and (e)
2 H deuterium signatures of streamflow, averaged groundwater wells (GW), hillslope spring, and averaged superficial saturation zone waters (%). Dates are given as day/month/year ; read 1/10/2008 as
1 October 2008.
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Flows were variable throughout the year, with high-flow
events occurring each month. The evapotranspiration
closely followed the temperature regime, with greatest values in summer (Figure 3b).
[27] Statistical summaries of the tracers in major water
stores and fluxes are given in Table 2; however, it is the
temporal dynamic of isotopic tracers that is most instructive. The isotopic composition of daily precipitation varied
throughout the year because of the relative uniformly distributed wet Scottish climate, though the greatest fluxes of
precipitation depleted in 2 H occurred during the winter
months and the greatest enriched fluxes occurred in
summer (Figure 3d). Although greatly damped, stream isotopes broadly reflect precipitation variation and seasonality
(Figure 3d). That said, the greatest enriched stream 2 H signatures were observed for a brief period in small events following a warm, dry spell in November 2008 and more
generally in summer 2009. Heavy winter storms cause a reversal of in-stream 2 H signatures to more negative values.
Despite the coarser weekly sampling during this period the
most depleted isotope characteristics are evident in events
between December and February, including the snowmelt
at the end of this period.
[28] Interestingly, even for flux-weighted averages, the
mean 2 H signature of stream water is not in equilibrium
with the mean precipitation 2 H signature (Table 2). This
might be due to the relatively short 13 month sampling period with larger and more enriched summer precipitations
than normal (Figures 3a and 3d). The averaged 2 H signatures of groundwater samples are generally less than those
of the stream, apart from periods following large winter
events when surface waters are evidently depleted (Figure
3e and Table 2). This also implies aquifers being preferentially recharged by larger winter storms. In contrast, despite
the shorter sampling period, the averaged saturation area
samples generally show a more enriched 2 H signature
compared to streamflow and groundwaters, except during
wet periods in the winter when the saturation of riparian
zones is extensive (e.g., Figure 1) and significant proportions of the catchment are contributing directly to streamflow [Tetzlaff et al., 2007b]. This shows the importance of
the saturation area not only for runoff generation but also
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as a mixing zone for new water entering the catchment as
precipitation and old water already stored. It appears that
the hillslope spring samples are slightly more enriched than
those of deeper groundwater in the wells, implying the
presence of shallower hillslope groundwater systems,
which is consistent with the original model storage concept
based on geochemical tracers and field observations [Birkel
et al., 2010a].
[29] Despite relatively few samples, the marked difference between the saturation zone and groundwater components is apparent from the mean alkalinity values of 37 and
416 eq L1, respectively (Table 2), and is consistent with
earlier studies [Soulsby et al., 2007]. We also find such differences in the 2 H signatures of averaged saturation area
waters and mean groundwaters (53% and 61%, respectively). The differences between the mean groundwater well
(63%) and hillslope spring (60%) 2 H signatures are
more subtle, but compared to the analytical error for 2 H,
they are still significant. Both groundwaters show little temporal variability throughout the year (Table 2). Therefore,
the definition of at least two distinct groundwater stores is
consistent in both alkalinity and 2 H measurements.
[30] Figure 4 shows the global meteoric water line
(GMWL) regression compared to the daily precipitation
signatures, which lie reasonably close together and only
slightly differ in their excess. On the basis of 2 H and 18 O
measurements, a local evaporation line (LEL) regression
was constructed (R2 ¼ 0.98) for stream water and compared to the isotope compositions of groundwaters and saturation area waters. The stream water samples alone are
located along a mixing line of water generated in colder
and warmer periods. However, it is the location of the saturation zone samples and groundwater samples along the
low gradient of the LEL (slope of 2.4) that indicate a contributing source to streamflow affected by isotopic fractionation processes. This is probably due mainly to
evaporation, though snowmelt and even sublimation may
also be important [Lee et al., 2009]. Even though the analytical error of isotope measurements has to be taken into
account, the saturation area water samples plot on the right
of the GMWL and along the LEL, whereas groundwater is
located close to the GMWL and overlaps with streamflow,
Table 2. Summary Statistics of the Tracers Alkalinity and Deuterium (2 H) in Stream Water, Precipitation (P), Snow, Groundwater
Wells (GW) 1 and 2, Hillslope Spring (HS), and Saturation Zonea
Sample
Mean
Minimum
Maximum
Standard Deviation
90th Percentile
10th Percentile
45.5
56.6
104.2
62.5
62.5
59.9
48.8
59.4
53
167.2
72.2
138.6
66.1
66.3
62
65.4
63.8
63.2
1.8
49.2
69.1
59.9
60.3
57.5
34.9
51.5
40.9
27.4
2.7
24.4
1.6
1.7
1.4
8.3
3
7.5
15.5
53.5
81.4
60.5
60
58.3
37.8
57.1
44.1
73.3
59.6
131.3
64.9
65
61.7
58.5
62.7
62.2
187.3
416
351
36.8
38.9
358
331
11.5
398
491
370
96.5
87.8
57.3
19.5
39.6
288.1
471
367
93.7
85
367
335
2.2
2
H (%)
P (n ¼ 212)
Stream (n ¼ 318)
Snow (n ¼ 8)
GW well1 (n ¼ 31)
GW well 2 (n ¼ 18)
HS (n ¼ 28)
Saturation zone 1 (n ¼ 18)
Saturation zone 2 (n ¼ 18)
Saturation zone 3 (n ¼ 18)
Alkalinity (meq L1)
Stream (n ¼ 47)
GW well 1 (n ¼ 4)
HS (n ¼ 3)
Saturation zone 3 (n ¼ 14)
a
Number n of samples is also given.
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Figure 4. Precipitation isotopes, average groundwater, and average saturation zone waters plotted
against the global meteoric water line (GMWL, line a) and the local evaporation line (LEL, line b) for
stream water isotopes.
suggesting fractionation processes occur in surface waters
of the saturated zone. Evaporative fractionation is most
likely to be greatest in the perennial open water system of
the saturation zone contributing directly to streamflow.
However, no vapor isotope measurements are available to
give clear evidence about significant or negligible fractionation due to evaporation and the effect on the streamflow
isotope composition. The difference in isotopic signature
between the stream, groundwater, and saturation zones further supports that saturation areas cannot simply be viewed
as an expression of the groundwater table, but rather must
be treated as distinct stores (especially during summer).
6. Incorporating New Insights From Time
Domain Tracers Into isoSAMdyn
[31] Figures 5a and 5b confirm the conclusions of earlier
work by Birkel et al. [2010a], showing that for the study
year, the basic SAMdyn model could successfully simulate
flows (range above threshold for discharge 0.6 < NS <
0.65 and 0.75 < VE < 0.8) and stream alkalinity (range
above threshold for alkalinity 0.6 < NS < 0.64) in the
Bruntland Burn in a way that was consistent with fieldbased process understanding. The number of behavioral parameter sets could be constrained from 6208 accepted discharge simulations to 1054 using alkalinity additionally to
discharge for calibration. The dynamics of the hydrograph
are simulated reasonably well, capturing peak flows and
recession periods (Figure 5a). The autumn and early winter
(September – December 2008) low-flow period is less well
reproduced than the summer 2009 period as low flows are
generally overestimated, indicating that certain storagerunoff dynamics are not captured. With regard to stream alkalinity simulations, these also capture the general dynamics, though with a tendency to underestimate the alkalinity
of low flows. This is a result of underpredicting the groundwater contribution to streamflow (Figure 5b). However, it
might also indicate the errors involved in the parameteriza-
tion of alkalinity in the model and that only weekly samples were available. However, the soil water concentration
of the quick flows below 100 eq L1 is simulated reasonably well, especially in the case of the February 2009 winter storm. The source area contributions over the following
3 months, peaking at 400 eq L1, are also well represented (Figure 5b).
[32] However, as Figure 5c shows, attempts to simulate
stream 2 H with the original SAMdyn model could not be
accepted as behavioral. The variations in simulated isotope
signatures are greatly exaggerated compared to those
observed. This suggests the need to incorporate an additional mixing volume (passive storage) into the model to
account for the damping of the incoming precipitation signal by increasing the residence time.
[33] In the revised model structure (isoSAMdyn ; Figure
2b) the hillslope storage is treated as unsaturated with a
high passive (immobile) water content (passive storage in
m3) and mixing volume to facilitate isotope damping, as
done by Barnes and Bonell [1996]. The groundwater and
riparian storages are treated as saturated (active storage in
m3) with negligible passive water available [Maloszewski
et al., 1992]. This also results in only one additional parameter. Because of the dynamic structure of the model, the
mixing volume parameter passiveSup was varied according
to the estimated saturation area extent time series dyn_
fSAT, where greater saturation area extents result in a
smaller hillslope storage area with potentially less passive
water available for mixing:
passive Sup ¼ Vini ð1 dyn fSATÞ ;
ð12Þ
where Vini is the calibrated initial mixing volume parameter
(m3) and dyn_fSAT volumetrically describes the saturation
area and hillslope area extent (percent catchment area). The
incorporation of passive storage into the water and mass
balance of equation (1) calculates the total hillslope storage
Sup as the sum of passive storage passiveSup and active
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Figure 5. SAMdyn (a) discharge and (b) stream alkalinity 5th and 95th percentile simulation envelopes
applying the discharge and alkalinity calibrated model. The dotted line at 37 eq L1 and the dashed
lines at 351 and 416 eq L1 indicate measured mean saturation zone, hillslope seepage (HS), and
groundwater (GW) alkalinity concentrations, respectively. (c) Incorporation of isotope mixing into the
dynamic saturation area model SAMdyn. The simulation of stream 2 H deuterium is demonstrated without further modifications to the original model concept (dashed line) and after an additional mixing volume in the hillslope storage (passive storage) was introduced (gray line) and applied with one accepted
parameter set. Dates are given as day/month/year; read 01/09/2008 as 1 September 2008.
hillslope storage activeSup. In this way, the water fluxes
through the active storage are not altered by the passive
storage. The active storage represents a state variable, and
the passive storage represents a calibrated parameter. Incorporating this additional mixing volume into the hillslope
storage water and mass balance of the isoSAMdyn model
improves the simulation of the overall stream isotope dynamics and event peaks substantially (Figure 5c). However,
this still could not capture the fine detail of the observed
daily isotope dynamics in the stream.
[34] A likely explanation for this is that waters of different
sources mix in the saturation zone before reaching the
stream. In the original version of SAMdyn, the groundwater
flow path was routed directly to the stream, bypassing the sat-
uration area zone without mixing (Figure 2a). While this was
adequate for simulating alkalinity (Figure 5b), it seems inadequate for simulating 2 H (Figure 5c). To explore the importance of the riparian area as a mixing zone, the model was
modified to simulate the upwelling and mixing of groundwater in the saturation zone (Figure 2b). Consistent with field
observations [Soulsby et al., 1998], a groundwater flux
(GWreturn, m3s1) was allowed to drain back into the riparian area when the groundwater store is full, facilitating additional mixing as well as Ql discharging directly to the stream.
[35] In addition, the different waters plotted against the
GMWL (Figure 4) indicated that fractionation due to evapotranspiration and snowmelt was probably influencing isotope signatures, with the open water system of the riparian
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saturation area being the most likely zone of influence.
Therefore, the potential effect of fractionation in the saturation areas was also incorporated in the final isoSAMdyn
model using a kinetic fractionation algorithm in the riparian
saturation zone mass balance. This allowed examination of
the enrichment effect of evaporation on the daily deuterium
signatures in the residual superficial waters prior to mixing
with incoming water fluxes and reaching the stream. The
isotopic signature of the loss term (evaporative flux) in the
riparian storage mass balance was calculated with the Craig
and Gordon [1965] model modified according to Gibson
and Edwards [2002] to directly utilize isotopic data (in %),
@E ¼
@Sat h@A "
;
1 h þ 103 "K
ð13Þ
where is the equilibrium liquid-vapor isotope fractionation, h is the atmospheric relative humidity normalized
(from 0 to 1) to the saturation vapor pressure at the temperature of the air-water interface, and @A is the isotopic composition of ambient moisture.
[36] In the absence of direct measurements, we assume
@A to be in equilibrium with the saturation area water,
@A ¼ @Sat [Jouzel and Merlivat, 1984], and
" ¼ "E þ "K
ð14Þ
(in %), where the total isotopic separation factor
"ð" ¼ 1Þ includes both equilibrium "E and kinetic
"K components.
[37] The equilibrium fractionation coefficient can be
estimated using empirical equations [Araguas-Araguas et
al., 2000]. The kinetic enrichment factor "E (%) depends
on the boundary layer conditions and the humidity deficit
h, estimated by
"K ¼ CK ð1 hÞ ;
ð15Þ
where experimentally determined CK values of 12.5% for
hydrogen are used to represent lake evaporation in the
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northern midlatitude hemisphere [Araguas-Araguas et al.,
2000]. The presence of saturation in the riparian zone
throughout the year makes this a reasonable first approximation for this particular study catchment.
[38] A constant snowmelt fractionation was also introduced into the model when positive air temperatures were
likely to generate melt. Because there were only 2 weeks of
significant snowfall in the catchment in February, we did
not incorporate a snowmelt routine in the model as maintaining low parameterization was a key objective. According to Cooper [1998], melt water from snow is an average
of 15% depleted for deuterium (at equilibrium). This coefficient was directly added to hillslope and saturation zone
fluxes in the water-isotope mass balance routine for inputs
during the snow period from 18 February to 3 March 2009.
[39] Figure 6 shows the simulated 2 H signatures in the
saturation area before and after fractionation occurs and after mixing of upwelling groundwater. Unfortunately, the
coarse, fortnightly sampling during this period misses much
of the fine-scale variability, but the pattern of effective fractionation is consistent with the data. This indicated the
observed snow period in winter (February – March) had
depleted 2 H signatures because of snowmelt fractionation,
while evaporative fractionation in early spring (May) and
summer (July – August) enriched the 2 H signatures. There
are also minor fractionation signals observable in spring and
late summer. Thus, incorporation of fractionation and the
mixing with upwelling groundwater apparently enabled isoSAMdyn to better capture the observed isotope dynamics in
the saturation areas. This can be seen in the simulated
responses for April, mid-May, and July 2009. Highly positive precipitation inputs probably caused the overestimation
of simulated 2 H signatures in June 2009.
7. Reconciling the Temporal Isotope Dynamics
With Conceptual Runoff Sources
[40] Parameter identifiability was assessed to evaluate
whether additional data to discharge helped constrain model
parameters and the model’s degrees of freedom [Fenicia
Figure 6. The effect of fractionation (snowmelt and evaporation) and mixing processes in the saturation zone (1 January to 7 October 2009) for the initial SAMdyn plus passive storage simulation (black
solid line) and for the simulation incorporating fractionation processes (gray line) and after mixing with
groundwater (GW) return flow (dashed line) simulated with the new isoSAMdyn model. Dates are given
as day/month/year; read 01/01/2009 as 1 January 2009.
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Figure 7. The cumulative efficiency (cum Eff) of model simulations is used to evaluate parameter
identifiability for the unconstrained total parameter space, the discharge- and alkalinity-constrained simulations, stream 2 H simulations, and the internally constrained stream 2 H simulations.
et al., 2008]. Figure 7 indicates parameter identifiabilities
expressed with cumulative efficiencies of the NS performance criteria for discharge, stream alkalinity, and stream
2 H simulations, applying the reconceptualized isoSAMdyn
model. Figure 7 shows that the model parameters except for
the recharge coefficient r and the isotope parameter upSd
are identifiable. However, multicriteria calibration of the
model against discharge and alkalinity significantly constrained parameter ranges (k1 and c) and increased identifiability (k1, k2, c, and ). The recharge parameter r remained
insensitive. Model calibration using internal state variables
in the form of hillslope and groundwater 2 H data also constrained the parameter range of upSd and increased identifiability compared to the initial parameter space (Figure 7).
[41] The overall simulation of dynamics in streamflow
2 H (range above threshold 0.2 < NS < 0.28 and 0.4 < R2
< 0.52) are the best possible with the current model structure. The high-flow variations were generally captured, but
daily variation in summer dynamics were particularly
poorly represented (Figure 8b). The relatively constant isotopic compositions of the hillslope spring (Figure 8c) and
groundwater (Figure 8d) were used to internally condition
the model. These match mean signatures (Table 2) within
analytical error intervals for the observed fortnightly 2 H
signatures of the hillslope spring and groundwater storages.
The simulation of observed fortnightly saturation area signatures ranged above threshold 0.4 < R2< 0.48, though
simulated values appear to underestimate the onset of fractionation processes in late April 2008 and to overestimate
them during midsummer (Figure 8e).
[42] Simulation of the fine-scale 2 H variability in daily
streamflow remains problematic, especially during periods
when fractionation caused by snowmelt or ET is important
(Figure 8b). This is evident from the 2 week snow period at
the end of February 2009 and during June and July in
summer 2009. Inclusion of fractionation processes during
these periods was needed to capture depleted signatures in
winter and more enriched signatures in summer. However,
this also leads to broader simulation bands for the saturation zone 2 H (Figure 8e) and stream 2 H (Figure 8b). This
perhaps suggests overestimation of the evaporative fractionation effect and underestimation of the damping due to
mixing processes taking place in the dynamic saturation
areas before water reaches the stream (Figure 8b).
Although, the 2 week snowmelt period partly consisted of a
rain on snow event not captured by the simple fractionation
coefficient, the incorporation of snowmelt and evaporative
fractionation improved the overall simulation of stream isotope signatures and is in line with observed data and process knowledge.
8.
Discussion
[43] The hillslope – saturation area – groundwater model
storage concept of the original SAMdyn model was
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Figure 8. (a) Measured discharge and simulated 2 H deuterium signatures in (b) stream water, (c) hillslope spring (HS), (d) averaged groundwater (GW), and (e) averaged saturation area water for the study
period 2008 – 2009, applying the multicriteria calibrated dual-tracer isoSAMdyn model. The simulation
envelopes indicate the 5th and 95th percentile prediction bounds. Dates are given as day/month/year;
read 01/09/2008 as 1 September 2008.
developed following approaches similar to those of Harris
et al. [1995], Seibert et al. [2003], and Fenicia et al.
[2008]. This approach integrated field observations and
tracer data for the BB catchment into a low-parameter
(five) conceptual model that could simulate streamflows
using the dominant geographic source areas of runoff in
terms of groundwater contributions and the nonlinear generation of overland flow from dynamic saturation areas
[Birkel et al., 2010a]. However, the same model structure
was unsuccessful in simulating the temporal variability of
isotope dynamics in both stream waters and the main catchment source areas, which became apparent when using
high-resolution precipitation and stream water samples.
Most problematic was the inability of the original model to
damp the incoming isotope signature. An additional storage
parameter was needed in the new isoSAMdyn model to
facilitate sufficient mixing to damp the temporal variation
in the deuterium signatures of precipitation inputs [Fenicia
et al., 2010]. In addition, the isotope data highlighted the
importance of the riparian saturation areas as zones for runoff generation and solute mixing [McGlynn and McDonnell, 2003; Tetzlaff et al., 2008b; Seibert et al., 2009].
Thus, simulations were improved by routing some groundwater contributing to a mixing zone in the saturated area
without changing the original source area conceptualization
[Anderson et al., 1997].
[44] Equally important to this improved representation
of mixing processes was the recognition of the fractionation process within the isotope dynamics. This was highlighted by the change of slope of the stream LEL compared
with the GMWL, representing the integrated effect of fractionation processes in the catchment due to evaporation in
the saturation zones and snowmelt [Gibson and Reid,
2009; Gibson and Edwards, 2002; Lee et al., 2009]. Integration of fractionation processes generally improved the
model simulations, and in the case of the snowmelt event,
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fractionation was necessary to capture the depleted stream
signatures. However, given the simplicity of the algorithm
used [O’Neil, 1968; Cooper, 1998; Luz et al., 2009], the
uncertainty is high, and the study period is too short to estimate fractionation via an isotope mass balance [He et al.,
2003]. Even though the incorporation of fractionation processes is in line with measured data and process understanding, more accurate means of quantification from direct
measurement are needed to avoid the extrapolation of
sparse and uncertain literature values. While this may
increase the number of model parameters, the importance
of fractionation processes in saturated zones may need to
be more carefully considered in studies that are attempting
to simulate isotopes in rainfall-runoff models. It is not necessarily the stream water itself that undergoes significant
evaporation, but even in the relatively wet and cool Scottish climate, the saturation zones effectively act as open
water systems throughout the year (comparable to shallow
lakes) and alter the stream isotope composition by contributing fractionated isotope content to the stream.
[45] The conceptualization of rainfall-runoff processes in
the isoSAMdyn model is broadly consistent with a fieldbased process understanding in the catchment [e.g., Malcolm et al., 2006; Soulsby et al., 2007; Tetzlaff et al.,
2007b]. As shown in other studies in the Scottish Highlands
[e.g., Soulsby et al., 1998, 2000], deeper groundwaters (often with a bedrock influence) are isotopically and geochemically distinct from spring seepage of shallower
groundwater systems (in hillslope colluvium) which drain
directly into the riparian zones (Figure 2b and Table 2).
However, the dynamics of riparian saturation zones are key
to understanding the hydrology and tracer dynamics of this
catchment. The dual-tracer approach has shown that the
model simulates observed tracer signatures of the dynamics
of different source components reasonably well. This better
reflects catchment behavior than only using geographic
source area tracers as in SAMdyn and thus justifies the use
of isotopic tracers as additional data in model assessment
[Seibert and McDonnell, 2002]. The use of soft data constrained model parameters and improved parameter identifiability (Figure 7), which, most importantly, conditioned
the model toward simulations consistent with process
knowledge. Furthermore, the use of isotope data of catchment stores constrained the tracer mixing parameter. This
might allow, in turn, more accurate estimations of catchment storage volumes [Kirchner, 2006]. The inferred passive storage (broadly identifiable between 2700 and 4200
mm, Figure 7) needed to damp tracer concentrations in the
model is an order of magnitude greater than the dynamic
storage variations as a result of seasonal variations of water
balance components. While these figures should be viewed
as indicative rather than definitive, such passive storage has
been shown in experimental studies [Engler et al., 2008],
and they are of the same order of magnitude as those inferred
by lumped parameter transit time modeling of the Bruntland
Burn using independent data [Soulsby et al., 2009].
[46] This study, for the first time, used both daily 2 H
and 18 O water stable isotopes collected over more than a
hydrological year to explore rainfall-runoff processes in a
Scottish upland catchment, applying an iterative model
approach testing different hypotheses of runoff generation
mechanisms. This unique data set is consistent with previ-
W02515
ous process conceptualizations based on geographic source
tracers and field studies in the area but emphasizes the need
to consider and further develop the passive storage concept
in catchments, the role of riparian saturation zones laterally
and vertically redistributing water and solutes to the stream,
and the role of isotopic fractionation processes due to
snowmelt and evaporation. Fractionation has rarely been
incorporated in catchment isotope-based process models
because of data constraints. Hence, the daily isotope record
refined the understanding of temporal rainfall-runoff dynamics compared to a coarser (e.g., weekly) sampling resolution [Birkel et al., 2010b].
[47] Even though much work remains on testing the
underlying assumptions of solute mixing [McGuire et al.,
2006; Fenicia et al., 2010], a novel element of this study
included the examination of the isotope dynamics of internal catchment stores, rather than just the rainfall-runoff
relationship [Bowden et al., 2001; Seibert et al., 2009].
Such measured data of internal catchment states could be
used more rigorously in the future to avoid subjectivity in
model calibration procedures [Winsemius et al., 2009].
There is also potential for more sensitive model evaluation,
especially when a better process representation consistent
with data does not necessarily improve statistical performance measures [Fenicia et al., 2010].
[48] Acknowledgments. This work has been funded by a Macaulay
Development Trust Ph.D. studentship in collaboration with the University
of Aberdeen. We are grateful to the Scottish Environmental Protection
Agency (SEPA) and the Fisheries Research Services (FRS) for access to
their data and use of experimental facilities. Alkalinity data for 2008/2009
and BB discharge data were provided by Mark Speed and Audrey Innes
from a project funded by the Leverhulme Trust. We thank Sheila Gibbs for
helping with the isotope analysis. The authors would also like to acknowledge that the review comments of John Selker, an associate editor, and
three anonymous reviewers significantly contributed to improving the original manuscript.
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C. Birkel and S. M. Dunn, Macaulay Land Use Research Institute,
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C. Soulsby and D. Tetzlaff, Northern Rivers Institute, School of Geosciences, University of Aberdeen, Aberdeen AB24 3UF, UK. (c.soulsby@
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